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Squared Frequency-Kt/V Murakami et al. Renal Replacement Therapy (2019) 5:8 https://doi.org/10.1186/s41100-019-0198-7 RESEARCH Open Access Squared frequency-Kt/V: a new index of hemodialysis adequacy—correlation with solute concentrations by computer simulation Kaya Murakami1, Kenichi Kokubo1,2,3*, Minoru Hirose1,2, Kozue Kobayashi1,2 and Hirosuke Kobayashi1,2 Abstract Background: In patients undergoing home dialysis, conventionally, Kt/V has been regarded as an index of the removal efficiency per dialysis session. However, more recently, it has been considered that the hemodialysis product (HDP), rather than the Kt/V, is better associated with the clinical symptoms and outcomes in patients undergoing short daily dialysis or nocturnal dialysis. Nevertheless, the HDP lacks a theoretical background, and it does not take into consideration the dialyzer clearance or patient’s body size. The aims of the present study were to clarify the theoretical validity of HDP focusing on its association with solute concentration by computer simulation and to propose a new index of hemodialysis adequacy. Methods: We used compartment models and calculated the time course of urea and β2 microglobulin (β2MG) concentrations to determine the peak concentrations and time-averaged concentrations at varying dialysis frequencies (n =2–7 sessions/week) and durations of dialysis per session (t = 1 to 8 h dialysis sessions). Results: It was found that the peak concentrations of urea and β2MG were significantly correlated with the HDP. Based on this, we theoretically extracted the factor related to the peak concentration and defined the squared frequency-Kt/V (sf-Kt/V), as a new index for determining hemodialysis adequacy (sf-Kt/V=n2Kt/V; K, clearance; V,solutedistribution volume; n,frequency;t, dialysis time); this index was well correlated with the peak concentrations of urea and β2MG, even when the values of K and V were changed. Conclusions: Since the sf-Kt/V is an index that reflects peak concentrations of urea and β2MG, which takes into account the dialysis frequency, session duration, dialyzer clearance, and the body weight of the patient, it will be a very useful tool for determining appropriate dialysis schedules and dialysis conditions for individual patients. Keywords: Kt/V, Hemodialysis product, Adequacy of dialysis, Home hemodialysis Background quality of life [7, 8], and lower cost [2, 3, 5]. In home Home hemodialysis has the advantage that dialysis sched- hemodialysis, since the dialysis schedule can be flexibly ule (frequency and duration of dialysis) can be changed at determined, a reliable index useful for determining the ap- the patients’ own convenience. Many modalities of dialysis propriate home dialysis modality, dialysis schedule (fre- suitable for home hemodialysis have been proposed, in- quency and duration), and dialysis treatment conditions is cluding short daily dialysis [1], nocturnal dialysis [2–5], required. and daily nocturnal dialysis [6]. Home hemodialysis has The Kt/V is a well-known index of the removal effi- been reported to be linked to increased survival [1, 7, 8], ciency per dialysis session. To compare different dialysis better blood pressure control [2], reduced left ventricular modalities, the standard Kt/V was proposed as an index mass [4], improved mineral metabolism [4], enhanced that can be uniformly used to measure and explicitly com- pare dialysis doses [9–11]. The use of this index was rec- ommended by the National Kidney Foundation Kidney * Correspondence: [email protected] 1Kitasato University Graduate School of Medical Sciences, Sagamihara, Japan Disease Outcomes Quality Initiative (KDOQI) guidelines 2Kitasato University School of Allied Health Sciences, Sagamihara, Japan [12] in 2006 and also by the most recent KDOQI in 2015 Full list of author information is available at the end of the article © The Author(s). 2019 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Murakami et al. Renal Replacement Therapy (2019) 5:8 Page 2 of 11 [13], to evaluate the optimal dialysis dose and schedule for currently available, it is difficult to select a dialyzer and frequent dialysis; however, it was still not widely used, operating condition suitable for short daily dialysis or probably because (1) its calculation process is quite nocturnal dialysis on the basis of the HDP. complex; (2) the calculation required values of single-pool The purpose of the present study was to explore a new Kt/V and equilibrated Kt/V to fit the original definition of index based on solute removal useful for ascertaining standard Kt/V, a mass generation per unit volume of body the adequacy of hemodialysis that would incorporate fluid normalized by the concentration; and (3) there is dialysis schedule (frequency and duration), the dialyzer little advantage to use standard Kt/V as an alternative to clearance, and patient’s body size. To this end, we first Kt/V Daugirdas which has already been widely used in sought to identify factors (such as the time-averaged daily clinical practices for three times a week schedule. concentrations/peak concentrations) that are strongly It was also reported that the hemodialysis product correlated with the HDP using a kinetic model. From (HDP), rather than the Kt/V, is better correlated with the our results, we developed an index that was also well clinical symptoms and outcomes in patients undergoing correlated with these factors and validated the index short daily dialysis and nocturnal dialysis, the modalities using a kinetic model. most often used for home hemodialysis [14]. HDP is an index of the adequacy of hemodialysis proposed by Methods Scribner and Oreopoulos [14] in 2002 as their opinion. Kinetic model for urea This index incorporates the dialysis frequency as an im- We used the single-pool model (Fig. 1a) and calculated portant variable: the time course of the concentrations of urea to deter- mine the peak concentrations and time-averaged con- HDP ¼ n2 t centrations under various dialysis schedules (Table 1). The change of the blood urea level during dialysis was where n is the dialysis frequency [times/week], and t is calculated using the following equation: the dialysis time per session [h/session]. VdC ðtÞ HDP has been proposed simply based on the very B ¼ −K C ðtÞþG dt u B u positive results with more frequent dialysis reported by K C ð Þ−G Kut G De Palma et al. [15], Buoncristiani et al. [16], Bonomini u B 0 u − V u That is, CBðtÞ¼ K e þ K . et al. [17], Pierratos et al. [2, 3], and Lockridge et al. u u [18]. The HDP has been shown to be well correlated And the change of the blood urea level outside the with the patients’ symptoms [14], and fewer symptoms period of dialysis was calculated by the following equation: [19–28] in dialysis patients has been reported in the treatment at HDP > 70, although these are retrospective VdC ðtÞ B ¼ −K C ðtÞþG observational studies where HDP has not been used as a dt u B u treatment criterion. Use of the HDP as an index of the Gu adequacy of hemodialysis has major limitations: it is an That is, CBðtÞ¼ V t þ CBðt1Þ empirical index that lacks a physiological or theoretical where CB is the blood urea level, CB(t1) is the blood background and ignores the effects of the dialyzer clear- urea level at the end of dialysis, Ku is the urea clearance, ance and patient’s body size. Therefore, although many and Gu is the endogenous production rate of urea. Using types of dialyzers (low flux to super high flux) are these equations, assuming Ku = 0, and a steady state (we AB Fig. 1 Schematic diagram of single-pool (one-compartment) model (a) and three-compartment model (b) Murakami et al. Renal Replacement Therapy (2019) 5:8 Page 3 of 11 Table 1 Setting conditions in the simulation Group A4 A5 A6 A7 A8 B4 B5 B6 B7 B8 C4 C5 C6 C7 C8 D3 D4 Dialysis frequencies [sessions/week] 2 2 2 2 2 3 33334444455 Dialysis time per session [h/session] 4 5 6 7 8 4 56784567834 HDP 16 20 24 28 32 36 45 54 63 72 64 80 96 112 128 75 100 Group D5 D6 D7 D8 E2 E3 E4 E5 E6 E7 E8 F1 F2 F3 F4 F5 F6 Dialysis frequencies [sessions/week] 5 5 5 5 6 6 66666777777 Dialysis time per session [h/session] 5 6 7 8 2 3 45678123456 HDP 125 150 175 200 72 108 144 180 216 252 288 49 98 147 196 245 294 Time course of changes in the solute concentrations for various dialysis schedule was calculated (the dialysis frequency varied from 2 to 7 per week and/or dialysis time per session from 1 to 8 h) repeatedly calculated the concentrations until the con- Runge-Kutta routine, using reported values [30] centrations at the beginning and end of the week were (Table 3). The time courses of the solute concentrations equal), the time courses of the urea concentrations were were calculated by the treatment conditions, such as the calculated by the treatment conditions and the produc- mass transfer coefficient between pools, solute produc- tion rate of urea [29] (Table 2). tion, and clearance of dialyzer. We compared the correlation between the peak Kinetic model for β2-microglobulin concentrations/time-averaged concentrations of solutes Three-compartment models (Fig.
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